The nil Hecke ring and singularity of Schubert varieties
The nil Hecke ring and singularity of Schubert varieties
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零赫克环和舒伯特簇的奇点
DOI：
10.1007/bf01232388
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发表时间：
1995
影响因子：
3.1
通讯作者：
Shrawan Kumar
中科院分区：
文献类型：
--
作者：
Shrawan Kumar
设G是一个半简单单连通复代数群，T≠B是一个极大环面和一个Borel子群。设N = Lie T是Lie代数Lie G的Cartan子代数，W:= N(T)/T是与（G， T）对相关联的Weyl群，其中N(T)是T在G中的归一化器。我们可以将任意元素\( \omega = \overline \omega \) mod T I W看作G/B的元素xo（用对应的德语字符表示），记为\( m = \overline \omega B \)。对于任意w I w，都有相关的Schubert变化\( {{\rm X}_{\omega }}: = \overline {B\omega B/B} \subset G/B \)，并且X w的t不动点（在正则左作用下）精确地为\( {\rm I}\omega : = \left\{ {o:\upsilon \in Wand\upsilon \leqslant \omega } \right\} \)。
Let G be a semi-simple simply-connected complex algebraic group and T ⊂ B a maximal torus and a Borel subgroup respectively. Let ŋ= Lie T be the Cartan subalgebra of the Lie algebra Lie G, and W:= N(T)/T the Weyl group associated to the pair (G, T), where N(T) is the normalizer of T in G. We can view any element \( \omega = \overline \omega \) mod T I W as the element (denoted by the corresponding German character) xo of G/B, denned as \( m = \overline \omega B \). For any w I W, there is associated the Schubert variety \( {{\rm X}_{\omega }}: = \overline {B\omega B/B} \subset G/B \) and the T-fixed points of X w (under the canonical left action) are precisely \( {\rm I}\omega : = \left\{ {o:\upsilon \in Wand\upsilon \leqslant \omega } \right\} \).